Just read somewhere that the shortest path between two locations is an arc and not a straight line! eli5 how an arc is the shortest path for planes.
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All the geometry you’re taught in school is Euclidean and assumes that everything is flat, this isn’t true for a lot of applications
In a flat open field if you need to get to a point 200 meters north and 300 meters west then the shortest path is a straight line between them that is 360 meters long
But what if you’re in a nicely gridded city and need to get to a point 2 blocks north and 3 blocks west? You can’t travel diagonally and thus need to cover 5 blocks not 3.6 blocks. This is [Taxicab or Manhattan Geometry](https://en.wikipedia.org/wiki/Taxicab_geometry)
For measuring on a sphere, you similarly can’t just take the straight distance between the two points because that would go through the sphere so you need to follow the surface. By following the surface your line is inherently curved in the same way our taxi cab can only travel north/south or east/west but not north east.
The arc is also super exaggerated when you look at it on a map because we have taken the much smaller polar regions and stretched them to be as wide as the equatorial regions. If you hold a string on a globe is looks a lot closer to the “straight” line you’re expecting and not the big sweeping arc that google maps shows you
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